1	Leaves dimorphic on adult plants, both submerged and floating leaves present		(2)
+	Leaves monomorphic, all submerged		(9)
2 (1)	Floating leaves less than 2.5 × 1.2 cm; submerged leaves sessile, filiform to linear, less than 2 mm wide, thin and translucent, not phyllodial		(3)
+	Floating leaves more than 3 × 1.5 cm; submerged leaves petiolate or sessile, ± lanceolate or oblong to elliptic, more than 5 mm wide or phyllodial, thick and opaque, 2-3 mm wide		(4)
3 (2)	Fruit with an obtuse or minutely undulate-toothed abaxial keel, beak ca. 0.3 mm.		16 P. octandrus
+	Fruit with a distinctly cristate abaxial keel, beak 1-1.2 mm.		17 P. cristatus
4 (2)	Submerged leaves phyllodial; floating leaves with a flexible joint and distinct angle at top of petiole immediately below blade often different in color.		18 P. natans
+	Submerged leaves with expanded blade; floating leaves without a joint and angle at top of petiole		(5)
5 (4)	Submerged leaves sessile		(6)
+	Submerged leaves petiolate		(7)
6 (5)	Plants usually unbranched, with distinct reddish tinge, particularly when dry; submerged leaves 7-33 mm wide, 9-19-veined, margin entire, apex obtuse; petioles of floating leaves shorter than blades.		14 P. alpinus
+	Plants usually branched, without a distinct reddish tinge; submerged leaves 5-12 mm wide, mostly 5-9-veined, margin minutely denticulate, apex mucronate; petioles of floating leaves usually longer than blades.		15 P. gramineus
7 (5)	Submerged leaves 9-13-veined; leaf tips mucronate.		12 P. wrightii
+	Submerged leaves (7-)11-21-veined; leaf tips acute to obtuse		(8)
8 (7)	Carpels (1 or)2(or 3); submerged leaf petiole 0.5-2.3 × length of blade.		19 P. distinctus
+	Carpels 4; submerged leaf petiole 0.2-1.5 × length of blade.		20 P. nodosus
9 (1)	Leaves broadly linear-oblong, lanceolate, elliptic, or ovate-oblong to suborbicular, mostly more than 5 mm wide		(10)
+	Leaves linear, 0.5-5 mm wide		(16)
10 (9)	Leaf margins serrate; fruit beak equal to or longer than body of carpel; plants occasionally forming hard, specialized turions.		9 P. crispus
+	Leaf margins entire or minutely denticulate; fruit beak shorter than body of carpel; plants not forming specialized turions		(11)
11 (10)	Leaves clasping stem, base rounded to cordate		(12)
+	Leaves not clasping stem, sessile, subsessile, or petiolate, base cuneate		(13)
12 (11)	Rhizomes spotted rusty red; leaves linear-lanceolate to ovate-oblong, 60-250 mm, entire, apex cucullate and splitting when pressed; stipules 10-80 mm.		10 P. praelongus
+	Rhizomes unspotted; leaves ovate or ovate-oblong to lanceolate, minutely denticulate, apex flat, not splitting when pressed; stipules 3-22 mm.		11 P. perfoliatus
13 (11)	Leaves long petiolate, petioles 16-140 mm.		12 P. wrightii
+	Leaves sessile, subsessile, or shortly petiolate, petioles 2-15 mm		(14)
14 (13)	Leaves subsessile or shortly petiolate, petioles 2-15 mm.		13 P. lucens
+	Leaves sessile		(15)
15 (14)	Plants usually unbranched, with distinct reddish tinge particularly when dry; leaves 7-33 mm wide, 9-19-veined, margin entire, apex obtuse.		14 P. alpinus
+	Plants usually branched, without a distinct reddish tinge; leaves 5-12 mm wide, mostly 5-9-veined, margin minutely denticulate, apex mucronate.		15 P. gramineus
16 (9)	Leaves serrulate; stipules shortly adnate to leaf base.		1 P. maackianus
+	Leaves entire; stipules free from leaf base		(17)
17 (16)	Leaves attenuate toward apex, with acuminate tips, slightly to distinctly falcate, (3-)5-7-veined with 2-18 additional sclerenchymatous strands.		2 P. oxyphyllus
+	Leaves parallel-sided at least for lower 3/4 of their length with obtuse to acute or mucronate tips, rarely acuminate, not falcate, 3-5-veined, sometimes with 8-32 additional faint sclerenchymatous strands		(18)
18 (17)	Stems slightly to strongly compressed, in upper part often flattened, 0.9-3.5 mm wide; leaves 3-5-veined with 8-32 additional faint sclerenchymatous strands		(19)
+	Stems terete, 0.3-1 mm in diam. throughout shoot; leaves 3-5-veined, lacking faint sclerenchymatous strands		(20)
19 (18)	Leaves 2.4-4.8 mm wide, with 12-32 sclerenchymatous strands in addition to vascular veins; stem in upper part 1.2-3.5 mm wide; fruit 3.4-4.6 mm.		3 P. compressus
+	Leaves 1.5-2.3 mm wide, with 8-14 sclerenchymatous strands in addition to vascular veins; stem 0.9-1.5 mm wide; fruit 2.8-3.8 mm.		4 P. mandschuriensis
20 (18)	Peduncle 0.4-1.2 × length of fruiting spike; leaves apically obtuse to rounded and very shortly and indistinctly mucronate, mostly 2.1-3.5 mm wide; stipules 1.1-3.5 mm wide.		5 P. obtusifolius
+	Peduncle 1.2-11 × length of fruiting spike; leaves apically acute to acuminate or sometimes distinctly mucronate, mostly 0.5-2.5 mm wide; stipules mostly. 3-1.3 mm wide		(21)
21 (20)	Stipules fused only at base but free from each other at upper part, split into 2 remnants, fibrous, markedly creamy white when dry; leaves (3-)5-veined.		6 P. friesii
+	Stipules not split into 2 remnants, intact stipules always fused throughout side toward leaf, not fibrous, green or greenish brown when dry; leaves 3-veined		(22)
22 (21)	Stipules connate, tubular at least when young, appearing as a closed ellipse when transversely dissected; leaves without rows of lacunae bordering midvein or rarely narrow rows present; midvein distinctly thickened toward leaf base; turions axillary; nodal glands absent or inconspicuous.		7 P. pusillus
+	Stipules convolute, appearing as an open ellipse or a short spiral when transversely dissected; leaves mostly with broad and conspicuous rows of lacunae bordering midvein; midvein not thickened toward leaf base; turions axillary and then nodal glands absent or turions terminal and then nodal glands well developed		(23)
23 (22)	Turions terminal; leaves parallel-sided, apex obtuse to acute; spike 4-8 mm in fruit; fruit with rounded back; nodal glands present at least on some nodes, often well developed.		8 P. berchtoldii
+	Turions axillary; leaves apically attenuate in upper 1/4 of their length, apex acuminate; spike 5-16 mm in fruit; fruit with obtuse to minutely undulate-toothed abaxial keel; nodal glands absent.		16 P. octandrus